A recipe for mac and cheese calls for 6 cups of pasta for every 4 cups of cheese. Suppose a restaurant is making a large batch of mac and cheese using 15 cups of cheese. How much pasta would they need?

Question

Start by labeling the double number line with the cups of cheese and cups of pasta that the recipe calls for.
Cheese (cups)
0
4
Pasta (cups)
0
6
You got it!
To find how many cups of pasta they’d need for 15 cups of cheese, it can be helpful to first find the unit rate, or the amount of pasta needed for 1 cup of cheese. Partition the number line to find the number of cups of pasta needed for every 1 cup of cheese.

Answer 1

To determine how much pasta the restaurant would need for 15 cups of cheese based on the original recipe ratio, we can start by finding the unit rate (the amount of pasta needed for 1 cup of cheese).

From the recipe, we know:

• 6 cups of pasta correspond to 4 cups of cheese.

To find the unit rate, we can divide the number of cups of pasta by the number of cups of cheese:

\[ \text{Pasta per cup of cheese} = \frac{6 \text{ cups of pasta}}{4 \text{ cups of cheese}} = \frac{6}{4} = 1.5 \text{ cups of pasta per cup of cheese} \]

Next, we can use this unit rate to find out how much pasta is needed for 15 cups of cheese:

\[ \text{Pasta needed} = 1.5 \text{ cups of pasta per cup of cheese} \times 15 \text{ cups of cheese} = 1.5 \times 15 = 22.5 \text{ cups of pasta} \]

So, the restaurant would need 22.5 cups of pasta to use with 15 cups of cheese.

Summary:

1. Pasta per cup of cheese: 1.5 cups of pasta for every cup of cheese.
2. Cups of pasta needed for 15 cups of cheese: 22.5 cups.